effects of activity complexes and active longitudes on variations in total solar irradiance

4
1063-7737/01/2707- $21.00 © 2001 MAIK “Nauka/Interperiodica” 0451 Astronomy Letters, Vol. 27, No. 7, 2001, pp. 451–454. Translated from Pis’ma v Astronomicheskiœ Zhurnal, Vol. 27, No. 7, 2001, pp. 528–532. Original Russian Text Copyright © 2001 by Mordvinov, Willson. INTRODUCTION A continuous monitoring of basic solar parameters in recent years and earlier long-term observations have shown that the Sun is a magnetic variable star in the full sense of the word: its luminosity, diameter, rotation parameters, and magnetic fields vary with an 11-year cycle of activity (Willson and Hudson 1991; Laclare et al. 1996; Howard and LaBonte 1980). Since these global variations exhibit a complex interrelation, thermo-magnetic phenomena span over the bulk of the Sun (Pipin and Kichatinov 2000). The solar magnetic fields have a multi-scale and hierarchical structure. Sunspots form structures that are seen as sunspot groups and activity complexes. Large sunspot groups concentrate within narrow intervals of heliographic longitudes, which are known as active longitudes. Long-lived longitudinal structures exist for many years, passing from one cycle of activity to another (Vitinskiœ et al. 1986; Bumba and Hejna 1991). These large-scale magnetic structures are characterized by rigid rotation with an angular velocity different from the Carrington velocity. The longitudinal organization of activity mapped by using various indices occasion- ally differs in details; nevertheless, general regularities can be found in the distribution of activity for its vari- ous manifestations (Vitinskiœ et al. 1986; Bumba and Hejna 1991). The active longitudes are often located at opposite heliographic longitudes, thus generating a 13.5-day periodicity of activity indices (Dodson and Hedeman 1968). Some active longitudes disappear for several years, and, subsequently, they are restored near their previous positions (Vitinskiœ 1997). This behavior of active longitudes can be explained as a manifestation of the fossil solar magnetic field (Kitchatinov et al. 2000). Occasionally, abrupt changes occur in the spatial distribution of activity: the zone of maximum activity passes from one interval of active longitudes to another, or comparatively short-lived active structures emerge. Since major solar flares also concentrate within the intervals of active longitudes, Bai (1988) called such regions on the Sun zones of superactivity or hot spots. He found that the 154-day periodicity played an impor- tant role in their evolution. A continuous wavelet anal- ysis of variations in total solar irradiance (TSI) has revealed cascades of spectral energy toward larger scales, which take place during the primary and sec- ondary maxima of cycle 22 in a time scale of 155 days (Willson and Mordvinov 1999). Here, we propose a numerical technique for time-longitude analysis of TSI variations; we have found large-scale thermal perturba- tions associated with long-lived magnetic structures. SPACIOTEMPORAL ANALYSIS OF TSI High-accuracy TSI measurements have been carried out during long-term space experiments since 1978, Effects of Activity Complexes and Active Longitudes on Variations in Total Solar Irradiance A. V. Mordvinov 1 * and R. C. Willson 2 1 Institute for Solar-Terrestrial Physics, P.O. Box 4026, Irkutsk, 664033 Russia 2 Research Center for Climatic Systems, Columbia University, Coronado, CA 92118, USA Received January 31, 2001 Abstract—A numerical technique of time–longitude analysis has been developed by studying the fine structure of temporal variations in total solar irradiance (TSI). This analysis produces maps of large-scale thermal inho- mogeneities on the Sun and reveals corresponding patterns of radiative excess and deficit relative to the unper- turbed solar photosphere. These patterns are organized in two- and four-sector structures and exhibit the effects of both activity complexes and the active longitudes. Large-scale patterns with radiative excess show a facular macrostructure caused by the relaxation of large-scale thermo-magnetic perturbations and/or energy output due to very large-scale solar convection. These thermal patterns are related to long-lived magnetic fields that are characterized by rigid rotation. The patterns with radiative excess tend to concentrate around the active longi- tudes and are centered at 103° and 277° in the Carrington system when averaged over the time-longitude dis- tribution of thermal inhomogeneities during activity cycles 21–23. © 2001 MAIK “Nauka/Interperiodica”. Key words: Sun, irradiance variations, large-scale magnetic fields * E-mail address for contacts: [email protected]

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Astronomy Letters, Vol. 27, No. 7, 2001, pp. 451–454. Translated from Pis’ma v Astronomicheski

œ

Zhurnal, Vol. 27, No. 7, 2001, pp. 528–532.Original Russian Text Copyright © 2001 by Mordvinov, Willson.

Effects of Activity Complexes and Active Longitudes on Variations in Total Solar Irradiance

A. V. Mordvinov1* and R. C. Willson2

1 Institute for Solar-Terrestrial Physics, P.O. Box 4026, Irkutsk, 664033 Russia2 Research Center for Climatic Systems, Columbia University, Coronado, CA 92118, USA

Received January 31, 2001

Abstract—A numerical technique of time–longitude analysis has been developed by studying the fine structureof temporal variations in total solar irradiance (TSI). This analysis produces maps of large-scale thermal inho-mogeneities on the Sun and reveals corresponding patterns of radiative excess and deficit relative to the unper-turbed solar photosphere. These patterns are organized in two- and four-sector structures and exhibit the effectsof both activity complexes and the active longitudes. Large-scale patterns with radiative excess show a facularmacrostructure caused by the relaxation of large-scale thermo-magnetic perturbations and/or energy output dueto very large-scale solar convection. These thermal patterns are related to long-lived magnetic fields that arecharacterized by rigid rotation. The patterns with radiative excess tend to concentrate around the active longi-tudes and are centered at 103° and 277° in the Carrington system when averaged over the time-longitude dis-tribution of thermal inhomogeneities during activity cycles 21–23. © 2001 MAIK “Nauka/Interperiodica”.

Key words: Sun, irradiance variations, large-scale magnetic fields

INTRODUCTION

A continuous monitoring of basic solar parametersin recent years and earlier long-term observations haveshown that the Sun is a magnetic variable star in the fullsense of the word: its luminosity, diameter, rotationparameters, and magnetic fields vary with an 11-yearcycle of activity (Willson and Hudson 1991; Laclareet al. 1996; Howard and LaBonte 1980). Since theseglobal variations exhibit a complex interrelation,thermo-magnetic phenomena span over the bulk of theSun (Pipin and Kichatinov 2000).

The solar magnetic fields have a multi-scale andhierarchical structure. Sunspots form structures that areseen as sunspot groups and activity complexes. Largesunspot groups concentrate within narrow intervals ofheliographic longitudes, which are known as activelongitudes. Long-lived longitudinal structures exist formany years, passing from one cycle of activity toanother (Vitinskiœ et al. 1986; Bumba and Hejna 1991).These large-scale magnetic structures are characterizedby rigid rotation with an angular velocity different fromthe Carrington velocity. The longitudinal organizationof activity mapped by using various indices occasion-ally differs in details; nevertheless, general regularitiescan be found in the distribution of activity for its vari-ous manifestations (Vitinskiœ et al. 1986; Bumba and

* E-mail address for contacts: [email protected]

1063-7737/01/2707- $21.00 © 20451

Hejna 1991). The active longitudes are often located atopposite heliographic longitudes, thus generating a13.5-day periodicity of activity indices (Dodson andHedeman 1968). Some active longitudes disappear forseveral years, and, subsequently, they are restored neartheir previous positions (Vitinskiœ 1997). This behaviorof active longitudes can be explained as a manifestationof the fossil solar magnetic field (Kitchatinov et al.2000). Occasionally, abrupt changes occur in the spatialdistribution of activity: the zone of maximum activitypasses from one interval of active longitudes to another, orcomparatively short-lived active structures emerge.

Since major solar flares also concentrate within theintervals of active longitudes, Bai (1988) called suchregions on the Sun zones of superactivity or hot spots.He found that the 154-day periodicity played an impor-tant role in their evolution. A continuous wavelet anal-ysis of variations in total solar irradiance (TSI) hasrevealed cascades of spectral energy toward largerscales, which take place during the primary and sec-ondary maxima of cycle 22 in a time scale of 155 days(Willson and Mordvinov 1999). Here, we propose anumerical technique for time-longitude analysis of TSIvariations; we have found large-scale thermal perturba-tions associated with long-lived magnetic structures.

SPACIOTEMPORAL ANALYSIS OF TSI

High-accuracy TSI measurements have been carriedout during long-term space experiments since 1978,

001 MAIK “Nauka/Interperiodica”

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MORDVINOV, WILLSON

(a)

(b)

(c)

(d)

(e)

1368

1366

1364

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1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000Years

TSI

, W m

–2δS

, W m

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1700 1750 1850 1900 19501800

090

180270360

090

180270360

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gitu

de, d

eg

Fig. 1. (a) A series of TSI measurements and (b) its filtered component. The (c) nonsmoothed and (d) smoothed time-longitude dis-tributions of brightness inhomogeneities. (e) The diagram of normalized brightness inhomogeneities. The maximum and minimumvalues of the gray scale for figures (c) and (d) should be multiplied by 0.75 and 0.25 W/m2, respectively. The periods of rigidly rotat-ing structures are given in days.

starting from the Nimbus-7 satellite. Subsequently, themeasurements were continued, and they are currentlybeing carried out with the radiometers mounted on foursatellites. Various radiometer calibration techniqueswere used to construct different versions of the com-posite TSI time series (Fröhlich and Lean 1998; Will-son 2000). Despite some differences in the fine struc-ture of these versions, their behaviors are in goodagreement with each other on a longer time scale (Will-son and Mordvinov 1999). Here, we perform a spa-tiotemporal analysis of the nineteenth version of thecomposite TSI time series (Fröhlich and Lean 1998)accessible via the Internet (http://www.pmodwrc.ch).A plot of the composite time series of TSI measure-ments is shown in Fig. 1a.

The TSI signal from the entire Sun is formed by theconvolution of the distribution of brightness inhomoge-neities over the solar disk with the weighting functionof limb darkening. Despite the fact that TSI is a globalindex, information about the spatial distribution of

brightness inhomogeneities can be extracted from tem-poral TSI variations due to solar rotation. Here, basedon wavelet filtering, we develop a numerical technique,which has allowed us to study the spatial distribution ofbrightness inhomogeneities and its changes by usingtemporal variations in TSI fine structure. By numericallyperforming deconvolution, an inverse operation for theconvolution of measurements, we can map long-livedbrightness inhomogeneities in heliographic longitude.

The main idea behind wavelet deconvolution is tofilter out the signal component associated with the TSIrotational modulation and to map this component as atwo-dimensional time–longitude diagram. A similardiagram for the mean solar magnetic field exhibits mul-timode solar rotation and its variations with an 11-yearcycle (Mordvinov and Plyusnina 2000). Orthogonalwavelet transformation is an efficient tool for filteringcomplex nonstationary processes. Here, we used thetechnique of decomposition into Daubechies orthogo-nal wavelets, which have good localization both in time

ASTRONOMY LETTERS Vol. 27 No. 7 2001

EFFECTS OF ACTIVITY COMPLEXES AND ACTIVE LONGITUDES ON VARIATIONS 453

and in time scales. A discrete wavelet transformationcan be written for TSI as a function of time as

(1)

where ψjk(t) are the wavelet functions that form anorthonormal basis, and the wavelet decompositioncoefficients are given by cjk = ⟨ fψjk⟩ (Astaf’eva 1996).The main effects of rotational modulation concentratein the range of time scales 13–30 days. Therefore,wavelet filtering should be performed by retaining onlythe coefficients that correspond to discrete time scalesof 8, 16, and 32 days when making inverse discretewavelet transformation. The filtered component thatcontains the main rotational effects is then

(2)

where 2 j correspond to the time scales (in days) onwhich the rotational modulation shows up. The filteredTSI component is shown in Fig. 1b. The nature and sta-tistical properties of the negative and positive TSI fluc-tuations are markedly different (Mordvinov 1996). Themaximum amplitude of the positive TSI fluctuationsreaches 1 W/m2, whereas the negative fluctuationsreach 2 W/m2.

Next, the filtered component was divided into sub-sets corresponding in time to Carrington rotations byusing interpolation and mapped rotation by rotation inthe form of a two-dimensional diagram. The time ofobservations within a Carrington rotation correspondsto a heliographic longitude. The time–longitude dia-gram constructed by using TSI deconvolution is shownon a gray scale in Fig. 1c. This diagram displays spatialbrightness inhomogeneities as deviations of the filteredcomponent from a mean TSI level, which slowly varieswith time. Positive deviations are shown in light tonesrelative to the 50% gray background, and negative devi-ations are shown in dark tones. In the time-longitudebrightness distribution, we can see a more or less regu-lar pattern, which is formed by long-lived structureswith reduced and excess radiation with respect to themean TSI level varying with an 11-year cycle. Thesestructures are associated with long-lived magneticstructures, activity complexes, and the macrostructureof facular fields. To study the large-scale organizationof such thermal structures and to reveal the effect ofactivity complexes (Obridko 1985), we smoothed thetime-longitude diagram with a window of three rota-tions by 40° in size. Figure 1d shows the smoothed dis-tribution of TSI deviations relative to the slowly vary-ing TSI component. In this diagram, regions whoseactivity complexes have lifetimes of 0.5–1 year showstand out as dark spots. Between these regions, we cansee areas with excess radiation; they are shown in lighttones and are apparently associated with the macro-structure of facular fields. These hot areas are clearly

S t( ) c jkψ jk t( ),j k, ∞–=

∑=

δS c jkψ jk,k ∞–=

∑j 3=

j = 5

∑=

ASTRONOMY LETTERS Vol. 27 No. 7 2001

seen at the epochs of minimum activity, when there areno sunspots.

In cycles 21 and 22, alternating two- and four-sectorstructures are seen in the longitude distribution of ther-mal inhomogeneities. The four-sector structures gener-ate a 13.5-day periodicity in TSI variations. For exam-ple, in the first half of 1984, when two deep dips in TSIwere observed, there was a distinct four-sector struc-ture in the time-longitude distribution of thermal inho-mogeneities; precisely at this time, an appreciable13-day variation appeared in the TSI wavelet spectrum(Willson and Mordvinov 1999). A continuous waveletanalysis of TSI variations has also shown that duringthe primary and secondary maxima of solar activity, atransition of spectral energy to longer time scalesoccurs (Willson and Mordvinov 1999). Interestingly,these cascades take place when the four-sector struc-ture is observed in the distribution of brightness inho-mogeneities, and they may be associated with cellswith a size of 90° in longitude.

To study the behavior of thermal inhomogeneities inheliographic longitude on a long time scale, we aver-aged the distribution of brightness inhomogeneities (seeFig. 1c) over the entire interval of observations. Figure 2shows the result of this averaging, which demonstratesthe existence of two sectors with excessive radiation inthe distribution of brightness in heliographic longitude.The TSI variations due to spatial brightness inhomoge-neities do not exceed ±0.06 W/m2. Remarkably, themaxima in the brightness distribution occur at longi-tudes of 103° and 277°, which are located within or inthe immediate vicinity of active longitudes. Duringcycles 21 and 22, the most stable active longitudesexisted in the intervals 80°–120° and 280°–320° (Vitin-skiœ 1997). Accordingly, in the time-longitude distribu-tion of TSI variations, long-lived structures with exces-sive and reduced radiation are often located within ornear these intervals, but, in general, the contribution ofthe regions with excessive radiation overcomponentsfor the deficit of radiation produced by sunspots.

–0.04

900 180 270 360

–0.02

0

0.02

0.04

0.06

S– , W

m–2

0.06

Longitude, deg

Fig. 2. The distribution of brightness inhomogeneities aver-aged for 1978–2000.

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THE ROTATION OF MAGNETO-THERMAL STRUCTURES

The structures that are horizontally arranged in thetime-longitude diagrams are characterized by the Car-rington rotation velocity. The regions of excessive andreduced radiation sometimes form inclined structuresin the time-longitude diagrams, pointing to the pres-ence of various modes of rigid rotation with periodsdifferent from the Carrington period. At the epochs ofminimum activity, the regions with excess radiationexhibit a systematic inclination, suggesting that theirrotation is slower than the Carrington rotation. By con-trast, the oppositely inclined diagonal structuresobserved at the beginning of cycle 22 suggest that theregions of reduced radiation rotate more slowly.

When the inclination of the structures and their rota-tion velocities are estimated, it does not matter whichevents (in amplitude) recurred; therefore, to representthe time–longitude distribution of brightness inhomo-geneities at different activity levels in a comparableform, we normalized the filtered TSI component to itsmaximum value within each rotation. Figure 1e showsthe time–longitude diagram for the normalized TSIcomponent. This distribution clearly reveals the rota-tional effects, irrespective of the phase of activity cycle(Mordvinov and Plyusnina 2000). At the epoch ofgrowing activity in 1988–1989, the regions withreduced radiation form inclined structures associatedwith activity complexes, whose rotation periods are 27.8and 26.4 days. At the epoch of minimum activity in1985–1987 and 1995–1996, the regions with excessradiation dominate and exhibit a faster rotation withperiods of 26.1, 26.6, and 26.8 days.

CONCLUSION

Our time–longitude analysis of variations in totalsolar irradiance has revealed large-scale structures onthe Sun with reduced and excess radiation relative tothe mean level, which varies with an 11-year cycle.During cycles 21–23, giant thermal spots, which wereseparated in heliographic longitude and associated withlong-lived magnetic structures, existed on the Sun.These structures were associated with active longi-tudes, activity complexes, and the macrostructure offacular fields. The large-scale magneto-thermal pertur-bations are characterized by a two- and four-sectorstructure in heliographic longitude. Although the distri-bution of brightness inhomogeneities is complex andnonstationary in pattern, averaging this distributionover the entire interval of observations clearly reveals aconcentration of the regions with excessive radiationwithin active longitude intervals; the maxima of thisdistribution occur at longitudes of 103° and 277°. Thethermal perturbations associated with activity com-plexes exhibit rigid rotation with an angular velocity

different from the Carrington velocity. The regions ofexcessive radiation trace the macrostructure of facularfields and may be attributable to the relaxation of large-scale thermo-magnetic perturbations and/or to the heatflux through giant subphotospheric convection.

ACKNOWLEDGMENTS

We are grateful to the staff of the World Data Centerin Switzerland for the opportunity to work with the TSIdata retrieved via the Internet (http://www.pmodwrc.ch).We thank V.M. Grigor’ev and L.L. Kitchatinov for adiscussion and helpful remarks. This work was supportedby the Russian Foundation for Basic Research (projectno. 99-02-16088) and the Program of State Support forLeading Scientific Schools (project no. 00-15-96659).The NASA provided support for Dr. Willson at ColumbiaUniversity under contact NAS5-97164.

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Usp. 39, 1085 (1996)].2. T. Bai, Astrophys. J. 328, 860 (1988).3. V. Bumba and L. Hejna, Bull. Astron. Inst. Czech. 42, 76

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5. C. Fröhlich and J. Lean, Geophys. Res. Lett. 25, 4377(1998).

6. R. Howard and B. J. LaBonte, Astrophys. J. Lett. 239, 33(1980).

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Translated by G. Rudnitskiœ

ASTRONOMY LETTERS Vol. 27 No. 7 2001